First of all, the serious neck problem is called Shermer's Neck after Michael Shermer's affliction on the 1983 RAAM, as seen in the link RC posted.
As for alleviating neck problems though, there are a number of things a person can do:
1) Do NOT wear a heavy helmet light. I used a rather heavy one on the PBP, and ditched it at the first control because I had already begun to develop some neck pain by then. Shortly after removing it, my neck felt fine again.
2) Stretch. Look up and down and from side to side frequently throughout the ride. Sit up and stretch, move your arms around and behind you etc. I try to do this as frequently as possible as I ride and when I remember, my whole upper body feels much better. Don't forget to stretch when you get off the bicycle as well.
3) Develop upper body strength through weightlifting or working at a job where you essentially do a form of weightlifting. You might also consider doing yoga or pilates throughout the year.
4) Raise your handlebars. If your handlebars are too low, you'll end up craning your neck too much to see.
5) Don't wear a visor on your helmet. I've tried to wear those visors and while they are great for blocking the sun and helping to stop me from squinting, I find I have to crane my neck too much to see properly and I end up with neck pain.
6) Keep glasses on bridge of nose so you are not looking over or under the frame.
7) If you sleep on a long randonnee, use your helmet, camelbak, handlebar bag, rolled up sweatshirt, inflatable pillow, or something that works for you to keep your spine straight and head comfortable.